WOLFRAM NOTEBOOK

P-x-y and T-x-y Diagrams for Vapor-Liquid Equilibrium (VLE)

​
diagram
P-x-y
T-x-y
temperature (°C)
115
​
The vapor-liquid equilibrium (VLE) behavior of an
n
-hexane/
n
-octane mixture is demonstrated in
P-x-y
and
T-x-y
diagrams. The blue line represents the liquid-phase boundary (bubble point) and the green line represents the vapor-phase boundary (dew point). Click and drag the black dot on either diagram and the bar chart shows the amounts of liquid (blue) and vapor (green) present; the system contains a total of 1 mol. The mole fractions of
n
-hexane in each phase (
x
H
for liquid phase,
y
H
for vapor phase) are also shown in the bar graph. Use sliders to vary the temperature for the
P-x-y
diagram or the pressure for the
T-x-y
diagram. This system is modeled by Raoult's law because an
n
-hexane/
n
-octane liquid phase is assumed ideal.

Details

The saturation pressure of component
i=(1,2)
is calculated using the Antoine equation:
sat
P
i
=
A
i
-
B
i
T+
C
i
10
,
where
i=1
for
n
-hexane and
i=2
for
n
-octane,
sat
P
i
is saturation pressure (bar),
A
i
,
B
i
, and
C
i
are Antoine constants, and
T
is temperature (°C).
Raoult's law is used to calculate the bubble-point and dew-point pressures using the
K
factors:
K
i
=
y
i
x
i
=
sat
P
i
P
,
where
y
i
is the vapor mole fraction and
y
1
+
y
2
=1
,
x
i
is the liquid mole fraction and
x
1
+
x
2
=1
, and
P
is the total pressure (bar).
The bubble-point pressure is calculated using
∑
K
i
x
i
=1
:
P=
x
1
sat
P
1
+
x
2
sat
P
2
.
The dew-point pressure is calculated using
∑
y
i
/
K
i
=1
:
P=
-1
y
1
sat
P
1
+
y
2
sat
P
2
.
A screencast video at[2] shows how to use this Demonstration.

References

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Prentice Hall, 2012 pp. 372–377.

External Links

Permanent Citation

Rachael L. Baumann, John L. Falconer, Megan Maguire, Nick Bongiardina
​
​"P-x-y and T-x-y Diagrams for Vapor-Liquid Equilibrium (VLE)"​
​http://demonstrations.wolfram.com/PXYAndTXYDiagramsForVaporLiquidEquilibriumVLE/​
​Wolfram Demonstrations Project​
​Published: June 5, 2014
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